Problem: Which of the following numbers is a factor of 162? ${5,6,8,11,12}$
Answer: By definition, a factor of a number will divide evenly into that number. We can start by dividing $162$ by each of our answer choices. $162 \div 5 = 32\text{ R }2$ $162 \div 6 = 27$ $162 \div 8 = 20\text{ R }2$ $162 \div 11 = 14\text{ R }8$ $162 \div 12 = 13\text{ R }6$ The only answer choice that divides into $162$ with no remainder is $6$ $ 27$ $6$ $162$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $6$ are contained within the prime factors of $162$ $162 = 2\times3\times3\times3\times3 6 = 2\times3$ Therefore the only factor of $162$ out of our choices is $6$. We can say that $162$ is divisible by $6$.